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A New Covariate Selection Strategy for High Dimensional data in Causal Effect Estimation with Multivariate Treatments

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arXiv 2023年

作者： Chen, Juan Zhou, Yingchun Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University China

Selection of covariates is crucial in the estimation of average treatment effects given observational data with high or even ultra-high dimensional pretreatment variables. Existing methods for this problem typically assume sparse linear models for both outcome and univariate treatment, and cannot handle situations with ultra-high dimensional covariates. In this paper, we propose a new covariate selection strategy called double screening prior adaptive lasso (DSPAL) to select confounders and predictors of the outcome for multivariate treatments, which combines the adaptive lasso method with the marginal conditional (in)dependence prior information to select target covariates, in order to eliminate confounding bias and improve statistical efficiency. The distinctive features of our proposal are that it can be applied to high-dimensional or even ultra-high dimensional covariates for multivariate treatments, and can deal with the cases of both parametric and nonparametric outcome models, which makes it more robust compared to other methods. Our theoretical analyses show that the proposed procedure enjoys the sure screening property, the ranking consistency property and the variable selection consistency. Through a simulation study, we demonstrate that the proposed approach selects all confounders and predictors consistently and estimates the multivariate treatment effects with smaller bias and mean squared error compared to several alternatives under various scenarios. In real data analysis, the method is applied to estimate the causal effect of a three-dimensional continuous environmental treatment on cholesterol level and enlightening results are obtained. © 2023, CC BY.

关键词： Mean square error

Risk Indicators and its application to Capital Allocation

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SSRN

SSRN 2023年

作者： Li, Danping Wang, Ying Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University China

Capital allocation is a core task in ffnancial reporting and risk management. This paper proposes two risk indicators, which can be applied to the ffeld of capital allocation modelling. We derive the optimal conditions for these two class of risk indicators and arrive at some properties for the corresponding allocation principles. Finally, we perform numerical calculation by examples to illustrate the effects of the parameters on the optimal allocation strategies, for instance, the independent exponentials and FGM bivariate model cases. © 2023, The Authors. All rights reserved.

关键词： Risk management

Regression models of Pearson correlation coefficient

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Statistical theory and Related Fields 2023年第2期7卷 97-106页

作者： Abdisa G.Dufera Tiantian Liu Jin Xu School of Stistis East China Normal University ShanghaiPeople's Republic of China Faculty of Industial Engineering and Management Technion-Israel Institute of TechnologyHaifalsrael Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE East China Normal UniversityShanghaiPeople's Republic of China

We propose two simple regression models of Pearson correlation coefficient of two normal responses or binary responses to assess the effect of covariates of ***-based inference is established to estimate the regression coefficients,upon which bootstrap-based method is used to test the significance of covariates of *** studies show the effectiveness of the method in terms of type-I error control,power performance in moderate sample size and robustness with respect to model *** illustrate the application of the proposed method to some real data concerning health measurements.

关键词： Binary responses bivariate normal responses Pearson correlation coefficient regression

The construction of two kinds of bijections in simple random walk paths

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arXiv 2019年

作者： Song, Sai Yao, Qiang Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University NYU-ECNU Institute of Mathematical Sciences NYU Shanghai

MSC Codes 60C05, 60J10It is known that for the 2n-step symmetric simple random walk on , two events have the same probability if and only if their sets of paths have the same cardinality. In this article, we construct two kinds of bijections between sets of paths with the same cardinality. The construction is natural and simple. It can be easily realized through programming. More importantly, this construction opens a door to prove that two events in the 2n-step symmetric simple random walk on Z have the same probability and some further related results. Copyright © 2019, The Authors. All rights reserved.

关键词： Random processes

Neural Networks Perform Sufficient Dimension Reduction

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arXiv 2024年

作者： Xu, Shuntuo Yu, Zhou Key Laboratory of Advanced Theory and Application in Statistics and Data Science MOE School of Statistics East China Normal University Shanghai China

This paper investigates the connection between neural networks and sufficient dimension reduction (SDR), demonstrating that neural networks inherently perform SDR in regression tasks under appropriate rank regularizations. Specifically, the weights in the first layer span the central mean subspace. We establish the statistical consistency of the neural network-based estimator for the central mean subspace, underscoring the suitability of neural networks in addressing SDR-related challenges. Numerical experiments further validate our theoretical findings, and highlight the underlying capability of neural networks to facilitate SDR compared to the existing methods. Additionally, we discuss an extension to unravel the central subspace, broadening the scope of our investigation. © 2024, CC BY.

关键词： Neural network models

A review of distributed statistical inference

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Statistical theory and Related Fields 2022年第2期6卷 89-99页

作者： Yuan Gao Weidong Liu Hansheng Wang Xiaozhou Wang Yibo Yan Riquan Zhang School of Statistics and Key Laboratory of Advanced Theory and Application in Statistics and Data Science–MOE East China Normal UniversityShanghaiPeople’s Republic of China School of Mathematical Sciences and Key Lab of Articial Intelligence–MOE Shanghai Jiao Tong UniversityShanghaiPeople’s Republic of China Guanghua School of Management Peking UniversityBeijingPeople’s Republic of China

The rapid emergence of massive datasets in various fields poses a serious challenge to tra-ditional statistical ***,it provides opportunities for researchers to develop novel *** by the idea of divide-and-conquer,various distributed frameworks for statistical estimation and inference have been *** were developed to deal with large-scale statistical optimization *** paper aims to provide a comprehensive review for related *** includes parametric models,nonparametric models,and other frequently used *** key ideas and theoretical properties are *** trade-off between communication cost and estimate precision together with other concerns is discussed.

关键词： Distributed computing divide-and-conquer communication-efficiency shrinkage methods nonparametric estimation principal component analysis feature screening bootstrap

Limit Properties of Record Numbers in Random walks

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arXiv 2024年

作者： Lu, Penghui Li, Yuqiang Yao, Qiang Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University Shanghai200062 China

In this paper, we systematically summarize and enhance the understanding of weak convergence and functional limits of record numbers in discrete-time random walks under Spitzer's condition, and extend these findings to σ-record numbers using similar methods. Additionally, we identify a sufficient condition for the existence of functional limits for record numbers in continuous-time random walks. Finally, we derive corresponding results for large deviations, moderate deviations, and laws of the iterated logarithm pertaining to record numbers in discrete-time random walks. Copyright © 2024, The Authors. All rights reserved.

关键词： Continuous time systems

CLIP-ReID: Exploiting Vision-Language Model for Image Re-Identification without Concrete Text Labels

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arXiv 2022年

作者： Li, Siyuan Sun, Li Li, Qingli Shanghai Key Laboratory of Multidimensional Information Processing China Key Laboratory of Advanced Theory and Application in Statistics and Data Science East China Normal University Shanghai China

Pre-trained vision-language models like CLIP have recently shown superior performances on various downstream tasks, including image classification and segmentation. However, in fine-grained image re-identification (ReID), the labels are indexes, lacking concrete text descriptions. Therefore, it remains to be determined how such models could be applied to these tasks. This paper first finds out that simply fine-tuning the visual model initialized by the image encoder in CLIP, has already obtained competitive performances in various ReID tasks. Then we propose a two-stage strategy to facilitate a better visual representation. The key idea is to fully exploit the cross-modal description ability in CLIP through a set of learnable text tokens for each ID and give them to the text encoder to form ambiguous descriptions. In the first training stage, image and text encoders from CLIP keep fixed, and only the text tokens are optimized from scratch by the contrastive loss computed within a batch. In the second stage, the ID-specific text tokens and their encoder become static, providing constraints for fine-tuning the image encoder. With the help of the designed loss in the downstream task, the image encoder is able to represent data as vectors in the feature embedding accurately. The effectiveness of the proposed strategy is validated on several datasets for the person or vehicle ReID tasks. Code is available at https://***/Syliz517/CLIP-ReID. Copyright © 2022, The Authors. All rights reserved.

关键词： Image segmentation

Disentangling the spatial structure and style in conditional vae

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arXiv 2019年

作者： Zhang, Ziye Sun, Li Zheng, Zhilin Li, Qingli Shanghai Key Laboratory of Multidimensional Information Processing Key Laboratory of Advanced Theory and Application in Statistics and Data Science East China Normal University Shanghai200241 China

This paper aims to disentangle the latent space in cVAE into the spatial structure and the style code, which are complementary to each other, with one of them zs being label relevant and the other zu irrelevant. The generator is built by a connected encoder-decoder and a label condition mapping network. Depending on whether the label is related with the spatial structure, the output zs from the condition mapping network is used either as a style code or a spatial structure code. The encoder provides the label irrelevant posterior from which zu is sampled. The decoder employs zs and zu in each layer by adaptive normalization like SPADE or AdaIN. Extensive experiments on two datasets with different types of labels show the effectiveness of our method. Copyright © 2019, The Authors. All rights reserved.

关键词： Mapping